Paint.NET

Inkscape

FTP / SFTP

Filezilla

IRC

X-Chat 2

Archiving

PeaZip

Fantastic archiving utility to extract and pack archives of an extensive amount of formats. PeaZip also features password protecting archives, keyfile support, system integration, a lovely interface, and much more.Download Page

Some more specialized free and open-source Microsoft Windows apps.

Note Taking

Freemind

An innovative application for note taking and outlining. Takes time to get used to, but some people swear by it.Download Page